Fitting continuum wavefunctions with complex Gaussians: Computation of ionization cross sections

Abstract

We implement a full nonlinear optimization method to fit continuum states with complex Gaussians. The application to a set of regular scattering Coulomb functions allows us to validate the numerical feasibility, to explore the range of convergence of the approach, and to demonstrate the relative superiority of complex over real Gaussian expansions. We then consider the photoionization of atomic hydrogen, and ionization by electron impact in the first Born approximation, for which the closed form cross sections serve as a solid benchmark. Using the proposed complex Gaussian representation of the continuum combined with a real Gaussian expansion for the initial bound state, all necessary matrix elements within a partial wave approach become analytical. The successful numerical comparison illustrates that the proposed all-Gaussian approach works efficiently for ionization processes of one-center targets.

31 pages, 8 figures

References in corpus (2)

• Gaussian continuum basis functions for calculating high-harmonic generation spectra
• Ab initio lifetime correction to scattering states for time-dependent electronic-structure calculations with incomplete basis sets

Cited by in corpus (5)

• A complex Gaussian approach to molecular photoionization
• Calculation of electron-impact and photo-ionization cross sections of methane using analytical Gaussian integrals
• Multicenter integrals involving complex Gaussian type functions
• On the use of complex GTOs for the evaluation of radial integrals involving oscillating functions
• A complex Gaussian representation of continuum wavefunctions respectful of their asymptotic behaviour